Solve 7(2x+3)(6x+2)-6x(2x+13)+8(7x+2)

$$7 ( 2 x + 3 ) ( 6 x + 2 ) - 6 x ( 2 x + 13 ) + 8 ( 7 x + 2 )$$

Evaluate

$$72x^{2}+132x+58$$

Solution Steps

Use the distributive property to multiply 7 by 2x+3.

$$\left(14x+21\right)\left(6x+2\right)-6x\left(2x+13\right)+8\left(7x+2\right)$$

Apply the distributive property by multiplying each term of 14x+21 by each term of 6x+2.

$$84x^{2}+28x+126x+42-6x\left(2x+13\right)+8\left(7x+2\right)$$

Combine 28x and 126x to get 154x.

$$84x^{2}+154x+42-6x\left(2x+13\right)+8\left(7x+2\right)$$

Use the distributive property to multiply 8 by 7x+2.

$$84x^{2}+154x+42-6x\left(2x+13\right)+56x+16$$

Use the distributive property to multiply -6x by 2x+13.

$$84x^{2}+154x+42-12x^{2}-78x+56x+16$$

Combine 84x^{2} and -12x^{2} to get 72x^{2}.

$$72x^{2}+154x+42-78x+56x+16$$

Combine 154x and -78x to get 76x.

$$72x^{2}+76x+42+56x+16$$

Combine 76x and 56x to get 132x.

$$72x^{2}+132x+42+16$$

Add 42 and 16 to get 58.

$$72x^{2}+132x+58$$

Expand

$$72x^{2}+132x+58$$

Solution Steps

Use the distributive property to multiply 7 by 2x+3.

$$\left(14x+21\right)\left(6x+2\right)-6x\left(2x+13\right)+8\left(7x+2\right)$$

Apply the distributive property by multiplying each term of 14x+21 by each term of 6x+2.

$$84x^{2}+28x+126x+42-6x\left(2x+13\right)+8\left(7x+2\right)$$

Combine 28x and 126x to get 154x.

$$84x^{2}+154x+42-6x\left(2x+13\right)+8\left(7x+2\right)$$

Use the distributive property to multiply 8 by 7x+2.

$$84x^{2}+154x+42-6x\left(2x+13\right)+56x+16$$

Use the distributive property to multiply -6x by 2x+13.

$$84x^{2}+154x+42-12x^{2}-78x+56x+16$$

Combine 84x^{2} and -12x^{2} to get 72x^{2}.

$$72x^{2}+154x+42-78x+56x+16$$

Combine 154x and -78x to get 76x.

$$72x^{2}+76x+42+56x+16$$

Combine 76x and 56x to get 132x.

$$72x^{2}+132x+42+16$$

Add 42 and 16 to get 58.

$$72x^{2}+132x+58$$